On the exit from a finite interval for the risk processes with stochastic premiums

Abstract

We consider the almost semicontinuous step-process ξ(t). The conditional characteristic functions of the jumps of ξ(t) have the form E [eiαξk /ξk > 0] = c(c − iα)−1. For such processes, the boundary functionals related to the exit from a finite interval are investigated.